ebook electrodynamics full pdf

() This is first-order differential equation, with a solution in homogeneous linear medium of () With Thus any initial free charge density f(0) dissipates in a characteristic time . This reflects the familiar fact that if you put some free charge on a conductor, it will flow out to the edges. The time constant  affords a measure of how \"good\" a conductor is: For a \"perfect\" conductor  =  and  = 0; for a \"good\" conductor,  is much less than the other relevant times in the problem (in oscillatory systems, that means i « l/); for a \"poor\" conductor, i is greater than the characteristic times in the problem (1/). At present we're not interested in this transient behavior- we'll wait for any accumulated free charge to disappear. From then on f = 0, and we have These differ from the corresponding equations for nonconducting media only in the addition of the last term in the fourth equation

Applying the curl to third and fourth equations, as before, we obtain modified wave equations for E and B: These equations still admit plane-wave solutions, ……………………………. …………………………

Potentials and fields The potential formulation Scalar and vector potentials Now we ask how the sources (p and J) generate electric and magnetic fields; in other words, we seek the general solution to Maxwell's equations. General solution of Maxwell’s equation could be achieved as follows: The Maxwell’s equations are Given (r,t) and J(r,t), what are the fields E(r,t) and B(r,t)? In the static case Coulomb's law and the Biot-Savart law provide the answer. What we're looking for, then, is the generalization of those laws to time-dependent configurations. This is not an easy problem, and it pays to begin by representing the fields in terms of potentials. In electrostatics This allowed us to write E as the gradient of a scalar potential:

. In electrodynamics this is no longer possible, because the curl of E is nonzero. In magnetostatics, If the divergence of magnetic field is zero, then it must be equal the curl of vector magnetic potential, i.e. if Then And, it must be Putting this into Faraday's law yields () () () () Here is a quantity, unlike E alone, whose curl does vanish; it can therefore be written as the gradient of a scalar, then

Then The potential representation automatically fulfills the two homogeneous Maxwell equations, the second equation and the third equation. How about first Maxwell’s equation and the fourth equation?. Putting the potential formulation of E into first Maxwell’s equation, we find that () () Putting Equations And

Into the fourth Maxwell’s equation, yields () ( ) Using the identity ( )() () ( )( ) These equations contain all the information in Maxwell's equations. Gauge transformations

Retarded potentials

References 1- John W. Jewett Jr. and Raymond A. Serway, 2010, Physics for Scientists and engineers, 8th ed., Brook/Cole, USA. 2- David J. GriffIths, 1999, Introduction to Electrodynamics, 3rd ed., Prentice Hall, New Jersey. 3- Costas J. Papachristou, 2020 , introduction to electromagnetic theory and the physics of conducting solids, Springer, Switzerland.

References list

Web sites https://ocw.mit.edu/courses/physics/8-07- electromagnetism-ii-fall-2012/ https://eopcw.com/find/course/257/courses https://nptel.ac.in/courses/115/101/115101004/